Maths Notation

Question 1

What does ℕ mean?

Answer 1

Natural numbers (positives) - infinite and countable

Question 2

What does ℤ mean?

Answer 2

Integers (whole numbers including negatives) - infinite and countable

Question 3

What does ℚ mean?

Answer 3

Rational numbers (fractions) - infinite but not countable

Question 4

What does ℝ mean?

Answer 4

Real numbers (all numbers that aren’t complex/ imaginary)

Question 5

What does ℤ^- mean?

Answer 5

Negative integers

Question 6

What does {} mean?

Answer 6

Empty set (nothing in it)

Question 7

What does ∅ mean?

Answer 7

Empty set (nothing in it)

Question 8

What is not an example of an integer?

Answer 8

A fraction!

Question 9

What must the powers of polynomials be?

Answer 9

Powers ∈ ℕ (can’t be negative or fractions!!)

Question 10

Is (2√3 - 2)/ (2√3 + 2) a rational or irrational number?

Answer 10

Irrational

Question 11

Solve the following inequality and write it in interval notation:
15 - (1+2x) ≥ 3(3x-10)

Answer 11

1) expand the brackets (left-hand one is multiplied by -1): 14-2x ≥ 9x-30
2) simplify: 44 ≥ 11x, 4 ≥ x
3) interval notation: x∈ (-∞,4]

Question 12

Solve the following inequality and write it in interval notation:
(2x+1)/2 - (x+1)/3 ≤ 5

Answer 12

1) cross multiply: 6x+3 - 2x+2 ≤ 5
2) simplify: 4x ≤ 25, x ≤ 25/4
3) interval notation: x∈(-∞,25/4]

Question 13

Work out the values of k for which the equation has no real roots. Give your answer in set notation:
x^2 + 2kx + 3 =0

Answer 13

b^2-4ac<0
(2k)^2 -4x1x3<0
4k^2 -12<0
k^2<3
k < ±√3
{k:k∈ ℝ, -√3<k<√3}